Do i pose the root bone too?
When you create a walk cycle in Pose mode, don't move the root, keep it still, this way, when you'll be back in Object mode, you'll be able to move the whole armature and the root won't go back and forth, it will comply to the animation you will give it in Object mode (like typically follow a curve).

You can move the root bone if you don't plan to move your object in Object mode, but in this case it generally won't be a cycle.